In the field of control engineering, PID controllers are familiar as position controllers for the exact positioning with the aid of electrical drives. The parameterization of such PID controllers is sometimes not easy, especially when very different operating states occur. Operating-state-dependent behavior of the system to be controlled due to non-linearities makes it impossible to find a set of parameters which is optimal in every operating state with respect to the control performance and the stability of the complete controller structure.
Thus, saturation effects ensure that the bandwidth of a current controller is worse at high currents than at low currents. In addition, at particularly low velocities, stick-slip effects may occur in a system to be controlled, which play no role at higher velocities in whose range only sliding friction prevails.
It is conventional to adapt gain factors in control loops to different operating states. U.S. Pat. No. 5,006,770 describes a velocity controller having a PI structure, whose I gain factor is set to be inversely proportional to the specific velocity in order to compensate for stick-slip effects. However, such a PI structure is not well-suited as a position controller, and in addition, it is not possible to compensate for saturation effects.